Test: Syllogisms - 1 - UCAT MCQ

(1) All fruits are apples — ✖. This is the converse; the statement gives Apples ⊂ Fruits, not Fruits ⊂ Apples.
(2) Some fruits are apples — ✔ if we assume apples exist (common exam convention). Since apples are a nonempty subset of fruits, some fruits are apples. (If you require strict formal existence, you would need an extra “there exists an apple” clause; exam convention usually assumes categories exist.)
(3) Some fruits are not apples — ✔. This is explicitly asserted by the added clause.
(4) All red apples are fruits — ✔. Every apple (whatever its colour) is a fruit; therefore any red apple is a fruit.

(1) All penguins are mammals — ✖. Not stated and false in taxonomy.
(2) No bird is a penguin — ✖. Contradicted by premise “some birds are penguins.”
(3) Some birds cannot fly — ✔. Explicitly stated.
(4) All penguins can fly — ✖. Premise includes non-flying birds (e.g., penguins), so you cannot infer they fly.
(5) Some birds are penguins — ✔. Explicitly stated.

(1) Some cats are cute — ✔. The cats that are black are cute because all black animals are cute.
(2) All cute animals are black — ✖. The premise is black → cute, not cute → black.
(3) Some black animals are cats — ✔. Direct from “some cats are black.”
(4) All black cats are cute — ✔. Black → cute, so black cats (a subset of black animals) are cute.
(5) Some cute animals are cats — ✔. Those black cats are cute, so some cute animals are cats.

(1) All flowers are blue — ✖. Only “some” are blue.
(2) No flower is blue — ✖. Contradicted by “some flowers are blue.”
(3) Some blue flowers are not roses — ✔. There exist blue flowers, and roses are not blue, so those blue flowers cannot be roses.
(4) All blue flowers are roses — ✖. Premise says roses are not blue, so this is impossible.

(1) Some educated people are not doctors — ✖. Not implied (there could or could not be educated non-doctors; not stated).
(2) Some doctors are not educated — ✖. Contradicts “All doctors are educated.”
(3) Some educated doctors are not successful — ✔. Explicitly stated.
(4) All successful people are doctors — ✖. Only “some successful people are doctors” is given, not all.
(5) Some successful people are doctors — ✔. Explicitly stated.

(A) All math students are chemistry or biology students — ✔. This is the statement restated.
(B) No biology student takes chemistry — ✖. Nothing in the statement restricts chemistry vs biology overlap.
(C) Some math students are not biology students — ✖. Not guaranteed; all math students could be biology students in theory.
(D) No student studies chemistry without math — ✖. Not implied.
(E) Some history students take math — ✖. No information about history is given.

(1) John will attend — ✔. John is a manager and all managers must attend, so John must attend.
(2) John is a good leader — ✖. Training requirement doesn’t entail leadership quality.
(3) All attendees are managers — ✖. Statement says all managers attend, not that only managers attend.
(4) All managers are good leaders — ✖. Training requirement ≠ guaranteed ability.
(5) John is the best manager — ✖. No ranking info provided.

(1) Sarah follows a strict diet plan — ✔. Direct instantiation of the universal.
(2) Sarah will become an Olympic champion — ✖. Diet alone does not guarantee that.
(3) All Olympic champions train regularly — ✖. Not stated.
(4) All athletes with strict diets become Olympic champions — ✖. Not stated.
(5) Sarah is the best athlete — ✖. No comparative info.

(1) Bob sat in seat number 2 — ✔. Explicitly stated.
(2) Emma sat in seat number 5 — ✔. Explicitly stated.
(3) Alice seat 4 — ✖. No info about Alice.
(4) Charlie seat 1 — ✖. No info about Charlie.

(1) All blue vehicles are buses — ✔. Follows from “only buses are blue.”
(2) All red vehicles are cars — ✔. Explicitly stated.
(3) Some blue vehicles are motorcycles — ✖. Contradicts “only buses are blue.”
(4) No red vehicle is a bus — ✖. Not implied: buses could be red too unless explicitly excluded; only blue ↔ bus and red → car are given, so (4) does not follow from the premises.